How do musicals get to Broadway? Let us count the ways.

Some bow first in Chicago or San Diego or Boston or Washington, usually at venues such as Arena Stage and the National Theatre. Some move uptown from off-Broadway. A few are born on the Great White Way itself, and still others map an international route to Times Square through London or Toronto or Sydney.

Now, one will get there by way of Woolly Mammoth Theatre. Or will if the theater gods — and D.C. audiences — are smiling.

In a first for the District’s singularly iconoclastic theater company, a new musical with Broadway dreams will be produced in Woolly Mammoth’s D Street NW headquarters. With performances to begin Sept. 15, the show even has a New York producer who’s vying for a home for it in one of Broadway’s 40-odd, highly sought-after theaters.

“A Strange Loop” is the musical, by Michael R. Jackson. The lift is major for a company far more experienced in mounting envelope-pushing plays than musicals; the last time Woolly tried a tuner, company officials said, was a revival 30 years ago of a spoofy “The Rocky Horror Show.”

This foray is spearheaded by Woolly’s artistic director, Maria Goyanes, who emphasizes there’s no attempt to turn her company into a “road house” for musicals seeking an out-of-town tryout. Rather, she argues, this is a natural extension of Woolly’s pursuit of material on the leading edge of the culture.

“What’s really exciting about it is that we can give resources over to that next step for Michael and Stephen,” she said, referring to Jackson and director Stephen Brackett. “This isn’t just putting it up to put it up. Michael really wants to work on it and refine it.”

Musicals reaching Broadway seem to be diversifying in theme and style, as indicated by some of the recent Tony winners for best musical — “Hadestown,” based on the Orpheus and Eurydice myth, and “Fun Home,” a lesbian coming-of-age story, among them — that have found enthusiastic audiences there. The avenues for landing on theater’s most prominent platform are branching off more idiosyncratically, too. It was not so long ago that a musical called “Next to Normal” premiered erratically off-Broadway, went out of town to Arena Stage for significant fixes and ended up on Broadway, with a Pulitzer Prize for drama to show for it.

“It’s certainly not a secret that I would be thrilled if it would go to Broadway,” said Jackson, a graduate of New York University’s musical theater program, who has been working on “A Strange Loop” on and off since 2001. “But there were still some things I wanted to keep working on.” Tightening the script and sharpening the humor are among the priorities.

“A Strange Loop” had an inaugural run last summer at Playwrights Horizons in New York. It’s a manifestly self-referential musical about a black, gay writer named Usher who works as a Broadway usher and is composing a musical about a black, gay writer named Usher who works as an usher and is composing a musical about . . . well, you get the drift. The show is a bit like staring into an M.C. Escher sketch or playing with a nest of Russian dolls, all set to show tunes. The wittily solipsistic premise extends to the cast, made up of Usher and his Thoughts, played by six actors assuming the various attitudes and neuroses that in turn make up Usher.

Many reviewers have expressed pleasure with Jackson’s irreverent intensity: Ben Brantley in the New York Times described the cheeky duality of the musical as “jubilantly anguished.” Goyanes liked what she saw, too, and had reason for special satisfaction: She knew Jackson and directed an embryonic version of “A Strange Loop” in New York in the mid-2000s. Earlier this year, Goyanes got in touch with producer Barbara Whitman, who had been involved with musicals like “Next to Normal,” “Fun Home” and “If/Then,” and had been a driving force behind “A Strange Loop” since seeing a developmental production of it in 2016.

Whitman was open to Woolly as a next step for the musical while she waited for a Broadway house to become available. No doubt a successful run at Woolly would boost its chances with Broadway’s major landlords. Also, “A Strange Loop” is un­or­tho­dox in theme and style, the type of show that might benefit from the cachet of a splash at a theater known for hipness among a younger crowd. “It gives you support for the production,” Whitman said. “It gives you an educated audience who knows what they’re going to see and they want to be a part of it. The audience is invested in helping you learn.”

Casting has not been announced, but the musical will be a pivotal part of the first half of Woolly’s 2020-21 season, which will also include co-sponsorship, with Shakespeare Theatre Company, of “The Jungle,” an immersive piece from Britain that just before Labor Day will turn Sidney Harman Hall into a refugee camp for actors portraying migrants from Africa and Asia. The new roster of offerings begins July 14 with a mini-festival that the company describes as a “summer of sex and body positivity”; it will consist of two solo shows (comic Jacqueline Novak’s “Get on Your Knees” and Ryan J. Haddad’s “Hi, Are You Single?”) and a late-night run of #TeamHusband’s “Rest of Gay DC Drag Show.”